(Solved): Physical chemistry 2. Answer all parts. Car airbags inflate when a small mass of sodium azide is ign ...

2. Answer all parts. Car airbags inflate when a small mass of sodium azide is ignited electrically, releasing nitrogen gas according to the following reaction: \[ 2 \mathrm{NaN}_{3}(\mathrm{~s}) \rightarrow 2 \mathrm{Na}(\mathrm{s})+3 \mathrm{~N}_{2}(\mathrm{~g}) \] which has \( \Delta_{r} H=42.6 \mathrm{~kJ} \mathrm{~mol}^{-1} \) and \( \Delta_{r} S=536.85 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \). (a) A particular car air-bag system contains \( 58.5 \mathrm{~g} \) of \( \mathrm{NaN}_{3} \), which at \( 25^{\circ} \mathrm{C} \) inflates the air-bag to a volume of \( 33 \mathrm{~L} \). Assuming it undergoes reversible expansion from an initial volume of \( 1 \mathrm{~L} \) determine the work performed and change in entropy during its inflation. Comment on the signs of these quantities. [15 marks] (b) State Hess's law and briefly discuss its importance in thermodynamics. Given that \( S^{\circ}(\mathrm{Na}(\mathrm{s}))=51.21 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \), and \( S^{\circ}\left(\mathrm{N}_{2}(\mathrm{~g})\right)=191.61 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \) determine the enthalpy of formation and standard entropy of \( \mathrm{NaN}_{3} \). [10 marks]